Quantitative Determination of Binding Affinity of δ-Subunit inEscherichia coliF1-ATPase

To study the stator function in ATP synthase, a fluorimetric assay has been devised for quantitative determination of binding affinity of δ-subunit to Escherichia coliF1-ATPase. The signal used is that of the natural tryptophan at residue δ28, which is enhanced by 50% upon binding of δ-subunit to α3β3γε complex.K d for δ binding is 1.4 nm, which is energetically equivalent (50.2 kJ/mol) to that required to resist the rotor strain. Only one site for δ binding was detected. The δW28L mutation increased K d to 4.6 nm, equivalent to a loss of 2.9 kJ/mol binding energy. While this was insufficient to cause detectable functional impairment, it did facilitate preparation of δ-depleted F1. The αG29D mutation reduced K d to 26 nm, equivalent to a loss of 7.2 kJ/mol binding energy. This mutation did cause serious functional impairment, referable to interruption of binding of δ to F1. Results with the two mutants illuminate how finely balanced is the stator resistance function. δ′ fragment, consisting of residues δ1–134, bound with the sameK d as intact δ, showing that, at least in absence of Fo subunits, the C-terminal domain of δ contributes zero binding energy. Mg2+ ions had a strong effect on increasing δ binding affinity, supporting the possibility of bridging metal ion involvement in stator function. High pH environment greatly reduced δ binding affinity, suggesting the involvement of protonatable side-chains in the binding site.

ATP synthesis by oxidative or photophosphorylation is catalyzed by the enzyme ATP synthase. In Escherichia coli the subunit composition is ␣ 3 ␤ 3 ␥␦⑀ab 2 c n . F 1 or F 1 -ATPase is the name given to the ␣ 3 ␤ 3 ␥␦⑀ subcomplex, which may be released from the membrane and purified in soluble form showing ATP hydrolysis activity. F o is the subcomplex that remains behind in the membrane after F 1 release. Consisting of ab 2 c n , it is responsible both for anchoring F 1 and for providing the pathway for protons to move through the membrane (1)(2)(3). ATP synthase is extraordinary because it acts as a rotary motor (4) with ATP hydrolysis on the three catalytic sites of F 1 located at ␣/␤ interfaces, providing the energy to drive rotation of the ␥-, ⑀-, and c-subunits (5)(6)(7)(8). These three subunits are firmly linked together and comprise the "rotor" of the motor (9 -11). ATP-driven rotation of the rotor, specifically of the c-subunit oligomeric ring, brings about proton efflux, and mechanisms for this proton transport have been suggested (11)(12)(13). It is widely assumed, although not yet demonstrated, that influx of protons through F o down the transmembrane proton gradient reverses the rotor, and that the rotational movement of ␥ within F 1 brings about ATP synthesis in the three catalytic sites. The mechanism by which ATP-driven rotation of subunits occurs, and the mechanism of rotation-driven ATP synthesis, are not yet understood and have most recently been discussed in Refs. 14 -16. It was apparent that a stator was required to counteract the rotor, and the stator is believed to be formed from the a-, b 2 -, and ␦-subunits (9,10,17,18). The stator is the least well understood part of ATP synthase in terms of structure. For a-subunit, no high resolution structure analysis is yet available, although topological models have been derived (11,19,20). It appears to be largely or entirely membrane-buried. The b-subunit dimer has been characterized biochemically and divided into functional domains (17,18,21), but no high resolution structure is yet available. Via its N-terminal region, bsubunit interacts with a-subunit within the membrane (22)(23)(24), whereas the C-terminal region of b is shown to interact with ␦ (21,25,26). Thus the b-subunit is pictured as being an elongated, helical molecule, positioned at one side of F 1 . NMR analysis has provided a high resolution structure for residues 1-105 of the ␦-subunit (27), but the structure of the remaining residues to the C terminus (residue 177) 1 is not yet known. Electron microscopic analysis has shown that ␦ is located at the top of F 1 (31), sitting presumably upon the "crown" formed by the N-terminal ␤-barrel domains of the ␣ 3 ␤ 3 hexagon (32).
Our understanding of the nature of the interaction between ␦ and F 1 remains rudimentary, however. Cross-linking studies showed proximity of the ␣and/or ␤-subunits to ␦, both in E. coli (33,34) and chloroplast enzyme (35). Other studies in E. coli enzyme implicated the ␣-subunit N-terminal region as being involved. Removal of the N-terminal 15 or 19 residues from ␣ by proteolytic digestion prevented binding of ␦ to ␣ 3 ␤ 3 ␥ complex (36). Cross-linking of an inserted Cys at residue ␣2 to a natural Cys in ␦ was obtained in high yield (37). The mutation ␣G29D rendered F 1 deficient of ␦-subunit and resulted in functional disruption, including partial loss of oxidative phosphorylation in cells, loss of F 1 binding to F o in vitro, and loss ATP-driven proton pumping in vitro (38). However, while the designation of the N-terminal region of ␣ as a "membrane-binding region" turned out to be well founded (38) (even though this region is actually the part of the enzyme most distant from the membrane) unfortunately none of the available x-ray structures show the extreme N-terminal residues of ␣ or any of ␦. Therefore no detailed model of the ␣/␦ interface can be assigned as yet. Questions that have not yet been answered are: 1) does ␦-subunit interact functionally with parts of ␤ as well as ␣, 2) are all three ␣-subunits (or ␣/␤ pairs) involved in binding one ␦ or is just one ␣ (or ␣/␤) sufficient, 3) what are the region(s) and residues of ␦ that bind to ␣ and/or ␤, and 4) what are the residues of the N-terminal of ␣ that are functionally directly involved in ␦-binding?
Understanding the manner in which the stator functions in ATP synthase is clearly important to understanding the overall process of ATP synthesis, and elucidating the nature of the ␦-F 1 interface in functional and structural terms is one facet of this problem. Our goal in this paper was to develop a quantitative binding assay to determine the binding affinity of ␦ under true equilibrium conditions and then to quantify the binding affinity accurately in wild-type and in the ␣G29D mutant. During the project we found that the mutation ␦W28L also impairs binding, suggesting that this region of ␦ is likely at or close to the ␦-F 1 interface. The C-terminal region of ␦ was found not to contribute any binding energy at the ␦-F 1 interface. An important role for Mg 2ϩ (or other divalent) ions is shown, and pH was found to profoundly influence ␦ binding.

EXPERIMENTAL PROCEDURES
Purification of F 1 , Purification of ␦-Subunit, and Preparation of ␦-depleted F 1 -E. coli F 1 was purified as in Ref. 39. ␦-subunit was purified as in Ref. 40 with minor modifications as follows. Plasmid pJC1 was transformed into strain AH3 (30) for expression, the gel filtration was on Sephacryl S100HR, and the peak from ion exchange or gel filtration was concentrated by ultrafiltration using Amicon YM10 membranes. ␦Ј fragment was purified using the same procedure, except pJC1 was transformed into strain DK8 (41). For purification of ␦W28L subunit, the mutation was constructed by directed mutagenesis using the oligonucleotide described previously (42) in an M13mp19 template containing an EcoRI-SmaI fragment from pJC1 (40). After mutagenesis the EcoRI-SmaI fragment was moved back to pJC1 creating the new plasmid pSWM101, which was transformed into strain AH3 and used for expression of ␦W28L subunit. ␦-depleted F 1 was prepared as in Ref. 43, except that the gel filtration column consisted of Sephacryl S300HR (1.5 cm ϫ 100 cm). The column buffer was 50 mM glycine/NaOH, pH 9.4, 2 mM EDTA, 1 mM ATP, and 10% glycerol at 20°C, and immediately after recovery the fractions were adjusted to pH 8.0 with 50 mM HEPES, pH 7.0.
E. coli Strains-Wild-type F 1 was purified from strain SWM1 (44). Trp-free F 1 was purified from strain pB0W1/DK8, created by transferring a Pme1-EagI fragment from plasmid p0W1(42) into plasmid pRLL2 (45) and transforming the resultant pB0W1 into strain DK8. ␦W28L F 1 was purified from strain pSWM92/DK8. pSWM92 was constructed by moving a PpuM1-SphI fragment from p0W1 into pBWU13.4 (46). ␤W107 F 1 was purified from strain pSWM86/DK8. pSWM86 was constructed by moving a Pme1-EagI fragment from pDP34N (47) into pRLL2. The following mutations were constructed by oligonucleotidedirected mutagenesis as in Ref. 45 using the respective oligonucleotides. 1) ␣L55W, GAAATGATCTCGTGGCCGGGTAACC, inserts a Trp (TGG) codon and also a new BssS1 site. The template was M13mp18 with an SphI-SalI fragment from p0W1, and after mutagenesis the mutation was moved into pB0W1 on an SphI-Csp45-1 fragment creating new plasmid pSWM89. 2) ␤F17W, GTTGACGTCGAATGGCCA-CAGGATGCCG, inserts a Trp codon and an Msc1/BalI site. The template was M13mp18 containing the ␤W107F mutation in a HindII-KpnI fragment from p0W1, and the mutations were moved back into pRLL2 on a Pme1-EagI fragment to create new plasmid pSWM87. 3) ␤Y26W, GGATGCCGTACCACGCGTGTGGGATGCTCTTGAG, inserts a Trp codon and both BstXI and Mlu1 sites. The template and procedure were as for ␤F17W, and the final plasmid was pSWM88. 4) ␣G29D, CTCA-CAACGAAGACACTATTGTTTCTG, adds a Bbs1 site. The template was the same as for ␣L55W mutagenesis above, and the ␣G29D mutation was moved into plasmid pSWM86 (above) on a SphI-Csp45-1 fragment to create new plasmid pSWM93. Each of the plasmids pSWM87,88,89, and 93 were transformed into strain DK8 for purification of F 1 .
Fluorescence Binding Assays-Tryptophan fluorescence was measured in a spectrofluorometer type SPEX Fluorolog 2 at 23°C. exc was 295 nm. The buffer was 50 mM HEPES/NaOH, 5 mM MgSO 4 , pH 7.0, unless noted otherwise. Binding of ␦ to ␦-depleted F 1 was measured by adding increasing concentrations of isolated ␦-subunit to 10 or 50 nM enzyme and monitoring the fluorescence at 325 nm. Background signals, including enzyme fluorescence and fluorescence of free ␦, determined in parallel control experiments, were subtracted. The bindinginduced increase in ␦ fluorescence was plotted versus the total ␦ concentration, and from the resulting curves K d values were determined by nonlinear regression. K d for binding of ␦W28L mutant subunit was estimated from competition experiments in which ␦-depleted F 1 was preincubated with a given concentration of ␦W28L subunit, and then wild-type ␦ was added. From the change in K d app for wild-type ␦ due to the presence of ␦W28L mutant, K d for the mutant was calculated.
Assay of ATP-driven Proton Pumping in Reconstituted Membrane Vesicles and Routine Procedures-Acridine orange fluorescence quenching was followed as an indicator of ATP-driven proton pumping (48). Membrane vesicles were stripped of F 1 by KSCN-extraction (48). For reconstitution of F 1 F o , stripped membranes (500 g of protein) were preincubated for 15 min at 30°C in a total volume of 500 l with F 1 (100 g) or ␦-depleted F 1 (100 g) plus appropriate amounts of ␦-subunit or ␦Ј fragment (10 g, unless otherwise indicated). 400 l of this mixture were added to 1.6 ml of assay buffer (100 mM HEPES/NaOH, 5 mM MgCl 2 , 300 mM KCl, pH 7.5). Acridine orange (4 M) fluorescence was continuously recorded in a spectrofluorometer type SLM AMINCO AB2 ( exc 430 nm, em 565 nm). Proton gradient formation was initiated by addition of 1 mM ATP and terminated by addition of 10 M CCCP. Assays of ATPase activity, protein concentration by Bradford assay, and SDS-gel electrophoresis on 10 -20% gradient gels were as described (49).

Strategy for Design of Assay to Determine K d of Binding
As discussed in the Introduction, current evidence favors the view that ␦-subunit binds to F 1 at the "top" of the molecule, distant from the membrane. Our initial approach was to insert single Trp residues into the N-terminal ␤-barrel domains of ␣or ␤-subunits, with the hope that upon binding of ␦, one or more of these would show perturbation of the Trp fluorescence signal. Conserved aromatic or leucine residues were targeted. The following mutations were made: ␣L55W, ␤F17W, and ␤Y26W. Each was expressed in the Trp-free background (42) previously used in this laboratory to characterize nucleotide-binding properties of the enzyme (e.g. Ref. 49). The Trp-free background contains the mutations ␦W28L/␣W513F/␥W108Y/␥W206Y/ ␤W107F and it was previously shown that Trp-free F 1 is functionally similar to wild-type (42). In addition the naturally occurring Trp at ␤107 was expressed alone in otherwise Trpfree background (we refer to this as the "␤W107" enzyme). After purification, all mutant enzymes showed normal subunit composition on SDS-gels. Properties of the mutant enzymes used in this work are shown in Table I. It may be seen that none of the enzymes containing single Trp residues or the Trp-free enzyme caused any major functional perturbation of ATP synthesis in cells as the growth yields were close to normal. Also, the specific activities of the purified F 1 were close to normal (the increased activity for Trp-free F 1 confirmed previous data (42)). Yields of the ␣L55W, ␤F17W, ␤Y26W, and Trp-free enzyme were 0.04, 0.085, 0.19, and 0.11 mg/g cells, respectively, which was significantly lower than wild-type (0.8 mg/g cells). However, the ␤W107 enzyme could be purified in good yield (0.41 mg/g cells).

Preparation of ␦-depleted F 1
To prepare ␦-depleted F 1 we used essentially the procedure of Smith et al. (43), in which F 1 is passed through a gel filtration column at pH 9.4, which causes the ␦-subunit to dissociate from the ␣ 3 ␤ 3 ␥⑀ complex. We found that complete ␦-depletion was not achieved with wild-type F 1 . However, complete depletion (as judged by Coomassie Blue-stained SDS gels) was achieved with the Trp-free enzyme, the mutants ␣L55W, ␤F17W, ␤Y26W, and the ␤W107 enzyme. The result of a ␦-depletion experiment using ␤W107 enzyme is shown in Fig. 1 lanes 1 and 2, and was typical for this group. Confirming the earlier report (43) we found that ␦-depletion by this procedure did not change the ATPase activity of F 1 . A common property of all the enzymes that could be efficiently depleted of ␦ by this procedure was that they contain the mutation ␦W28L in the ␦-subunit. We therefore constructed an enzyme that was wildtype except for the ␦W28L mutation and found that it too could be readily depleted of ␦-subunit. Thus residue ␦Trp-28 appeared to contribute to enhanced affinity of binding of ␦-subunit to F 1 , and use of the mutant ␦W28L was valuable for ␦-depletion.

Expression and Purification of ␦-Subunit
We used essentially the method reported by Dunn and Chandler (40) in which ␦-subunit expression from plasmid pJC1 is induced by isopropyl thiogalactoside. Plasmid JC1 was transformed into strains DK8 (⌬uncB-uncC) or AH3(⌬uncFH). Growth conditions and purification of ␦ were essentially as described (40). In the original procedure a proteolytic fragment named ␦Ј, consisting of residues 1-134 of ␦-subunit (27) was formed and had to be separated from intact ␦. Here we found that using the DK8 background, only ␦Ј was present, and it could be purified to homogeneity readily (Fig. 1, lane 3). In contrast, in the AH3 background, mostly intact ␦ and little ␦Ј was present, and the intact ␦ could be readily purified (Fig. 1, lane 5) in high yield (5.0 mg/liter cells). We also introduced the ␦W28L mutation, allowing purification of this mutant ␦-subunit (Fig. 1, lane 4).

FIG. 2. ATP-driven proton-pumping in reconstituted F 1 F o .
A, membrane vesicles were stripped of F 1 by KSCN treatment, then reconstituted with wild-type ␦-depleted F 1 (trace 1), intact wild-type F 1 (trace 2), or wild-type ␦-depleted F 1 incubated with wild-type ␦-subunit (trace 3). The traces show acridine orange fluorescence upon addition of ATP. A quench of fluorescence indicates proton uptake into the reconstituted vesicles. For details, see "Experimental Procedures." B, wildtype ␦-depleted F 1 was incubated with increasing concentration of purified wild-type ␦-subunit and reconstituted with stripped membranes. The percent quench of acridine orange fluorescence after addition of ATP is plotted against the molar ratio of ␦/F 1 . stituted for ␦, however, no reconstitution of function occurred. Using this method we found that all of the mutant F 1 preparations containing single Trp and Trp-free F 1 gave 50 -85% quenching of acridine fluorescence quenching upon rebinding to stripped membranes either before ␦-depletion or after ␦-depletion followed by incubation with wild-type or ␦W28L ␦-subunit. Therefore all of these mutant enzymes were functionally competent. The experiment also showed that the procedure used for ␦-depletion did not cause functional impairment and that our purified ␦ preparations were fully active.
We investigated whether this procedure could be used to determine stoichiometry and/or affinity of binding of ␦ to ␦-depleted F 1 . Fig. 2B shows a typical titration experiment in which increasing amounts of wild-type ␦-subunit were mixed with wild-type ␦-depleted F 1 and stripped membranes. The curve shows that saturation was reached at a stoichiometry of less than 1 mol of ␦ per mol of added ␦-depleted F 1 . This result ensues because the F o binds F 1 -␦ complex preferentially, and the assay requires that F 1 is present in excess over F o . Thus this assay cannot be used to determine accurately the affinity of binding of ␦ to F 1 .

Flurorescence Properties of F 1 and ␦-Subunit
The environment of the introduced Trp in the mutant enzymes varied from unpolar (␤F17W) to moderately polar (␤Y26W; max values given in Table I). Each of the enzymes, ␣L55W, ␤F17W, ␤Y26W, and ␤W107, was ␦-depleted and then mixed with purified ␦W28L ␦-subunit (which lacks Trp and therefore has no intrinsic Trp fluorescence of its own as seen in Fig. 3, trace 1). In no case was any change in fluorescence spectrum seen (data not shown). Therefore none of these single Trp residues was responsive to addition of ␦-subunit, and it appeared binding of ␦ caused no changes of the environment of these residues within the N-terminal ␤-barrel domains of the ␣and ␤-subunits, indicating conformational rigidity of the F 1 crown.
However, when the same experiment was repeated using wild-type ␦ instead of ␦W28L, in every case an enhancement of the total fluorescence was seen. Fig. 3 shows typical spectra obtained using the ␤W107 enzyme, and the same results were seen with ␣L55W, ␤F17W, and ␤Y26W enzymes. Fig. 3, trace 2 shows the intrinsic fluorescence of purified wild-type ␦, which has a maximum at 326 nm, showing that the single Trp in wild-type ␦ resides in a relatively unpolar environment. Trace 3 is the spectrum obtained upon mixing ␦-depleted ␤W107 F 1 with wild-type ␦ after subtraction of the contribution of ␦-depleted ␤W107 F 1 alone. The experiment shows that upon binding of ␦ to ␦-depleted F 1 , a strong enhancement (ϩ50%) of the fluorescence of residue ␦Trp-28 occurs accompanied by a blueshift of 4 nm. The same enhancement of residue ␦Trp-28 fluorescence was seen using ␦-depleted Trp-free and wild-type F 1 (data not shown). The results show that the environment of residue ␦Trp-28 becomes more unpolar upon binding to F 1 and, importantly, show that the fluorescence change of this residue provides a sensitive equilibrium binding assay for ␦ binding to F 1 .

Determination of Affinity of Binding of Purified ␦-Subunit or ␦Ј to ␦-depleted F 1 by Fluorescence Assay
We chose to use the ␤W107 enzyme for most assays for the following reasons. As noted above, the ␤W107 enzyme was obtained in good yield. Also, because its intrinsic fluorescence was 60% lower than that of wild-type enzyme, this meant that the correction factor upon subtraction of the intrinsic F 1 fluorescence (see above) was lower. It might seem that Trp-free F 1 would provide even greater advantage; however, this was counterbalanced by the low yield of this enzyme. However, we wish to emphasize here that binding measurements were made with the ␤W107, ␤Y26W, Trp-free, and wild-type enzymes, and all showed essentially identical affinity (K d ) for binding of wildtype ␦-subunit as determined in titration experiments. Fig. 4A shows typical titration curves obtained when ␤W107 (trace 1) or wild-type (trace 2) ␦-depleted F 1 was titrated with FIG. 3. Fluorescence spectra of purified ␦-subunit and of ␦-subunit bound to ␦-depleted F 1 . Corrected spectra are shown. Trace 1, purified ␦W28L subunit; trace 2, purified wild-type ␦-subunit; trace 3, purified wild-type ␦-subunit mixed with ␦-depleted ␤W107 F 1 (ratio 1 mol/mol). Note that the contribution of the ␤W107 F 1 fluorescence alone (in absence of ␦) has been subtracted from trace 3.
wild-type ␦. In these experiments the concentration of ␦-depleted F 1 was 50 nM at pH 7.0 with 5 mM Mg 2ϩ present. The titration curves were fitted by a model assuming n binding sites. The curves appear "stoichiometric," i.e. there is a closeto-linear approach to saturation plateau, which is reached at a ratio of 1 ␦ per F 1 (mol/mol), and in all cases the calculated value of n was 1.0 or very close to 1.0. Fig. 4B shows titration curves using 10 nM ␦-depleted ␤W107 F 1 (trace 1) or Trp-free ␦-depleted F 1 (trace 2) with wild-type ␦. These more rounded curves yielded K d values similar to those calculated from Fig.  4A data. Lower protein concentrations could not be used due to loss of sensitivity. Fig. 4B, trace 3 shows a control experiment in which ␦-depleted ␤W107 F 1 was titrated with purified ␦W28L subunit, yielding no enhancement of fluorescence.
Calculated K d values for binding of wild-type ␦ to wild-type, ␤W107, Trp-free, and ␤Y26W ␦-depleted F 1 are shown in Table  II, lines 1-4. We note that in no case was there any indication of additional binding sites, and from the results we can state that if such binding sites occur their K d values are Ͼ1 M.
The affinity for binding of ␦Ј fragment was measured by the same technique (see Fig. 4A, trace 3), and K d was found to be 1.4 nM for binding to ␤W107 F 1 (Table II, line 5). This experiment showed that under the assay conditions in Fig. 4, none of the binding energy between ␦ and F 1 is contributed by the C-terminal part of ␦.

Conditions That Affect the Strength of ␦ Binding to F 1
The purification procedure for E. coli F 1 involves preparation of membrane vesicles enriched in F 1 F o followed by release of the F 1 in presence of EDTA to chelate Mg 2ϩ ions. Additionally, F 1 may be depleted of ␦-subunit by gel filtration at high pH values (see "Experimental Procedures"). Thus it was anticipated that both pH and Mg 2ϩ concentration would affect the strength of ␦-binding. Table III shows values of K d for binding of wild-type ␦ to ␦-depleted F 1 under a range of pH values in presence or absence of 5 mM Mg 2ϩ ions. It may be noted that Mg 2ϩ ions had a large effect at all pH values. In the presence of Mg 2ϩ , binding affinity (K d ) was found to lie in a narrow range between pH 6.0 and 9.0 but increased at pH 9.4 to 16.6 nM. pH 9.4 is the condition for preparation of ␦-depleted F 1 . In the absence of Mg 2ϩ , all K d values were increased, and the influence of higher pH on K d values became very marked indeed. Addition of ADP (1 mM) in presence of 5 mM Mg 2ϩ ions at pH 7.0 had no effect on the binding curve or calculated K d values.

Mutations That Impair ␦-Binding
The ␣G29D Mutation-Originally identified by random mutagenesis (38), the ␣G29D mutation is the only mutation yet known to cause functional defects specifically derived from disruption of ␦-binding to F 1 . These defects include impairment of binding of F 1 to F o , ATP-driven proton pumping, and oxidative phosphorylation (38). In contrast, for example, the ␣Q2C mutation did not cause functional defects, although cross-linking of the introduced ␣Cys-2 to natural Cys in ␦ could be readily achieved (37), showing proximity of the introduced Cys to ␦. Thus the region around ␣Gly-29, and perhaps residue ␣Gly-29 itself, is likely involved in ␦-binding. We therefore wished to define the effects of the mutation in quantitative terms. For this purpose the ␣G29D mutation was combined with the ␤W107 mutation in an otherwise Trp-free background. As expected the growth yield of strain ␣G29D/␤W107 was significantly lower than wild-type or of ␤W107 alone (Table I). Purified ␣G29D/␤W107 F 1 retained ATPase activity (Table I); however, in the ATP-driven proton-pumping assay conducted as in Fig. 2, ␣G29D/␤W107 F 1 gave only 12% quench of acridine orange fluorescence in presence or absence of excess added wild-type ␦. ␦-depleted ␣G29D/␤W107 F 1 was prepared and titrated with wild-type ␦ (Fig. 5), yielding a K d value of 25.5 nM as compared with a value of 1.4 nM for wild-type or ␤W107 alone (see above). Thus a diminution of strength of binding of ␦ to F 1 of around 20-fold is caused by ␣G29D, and this is sufficient to cause defects in F 1 F o function easily detectable in vitro and in vivo. It may also be noted that titrations of the ␣G29D/ ␤W107 mutant enzyme with wild-type ␦-subunit consistently gave greater fluorescence enhancement than that seen with wild-type, Trp-free, or ␤W107 enzymes, by 1.4-fold, as if the ␣G29D mutation itself were directly affecting the environment of the ␦Trp-28 residue.
␦W28L Mutation-We had a strong indication that the ␦W28L mutation weakened binding of ␦ to F 1 from the fact that it facilitated preparation of ␦-depleted F 1 . To assay the K d of binding of the mutant ␦ we used a competition assay in which titrations of wild-type ␦ to ␦-depleted ␤W107 F 1 were carried out in the presence of different fixed concentrations of added ␦W28L. The results of three experiments (not shown) gave a K d of 4.6 nM (Table II). Thus the ␦W28L mutation weakens binding by 3-to 4-fold. This apparently is sufficient to allow more efficient ␦-depletion of F 1 but not sufficient to cause significant functional impairment in the cell or in ATP-driven proton pumping assays in vitro. DISCUSSION We report here a novel assay for quantitative determination of binding affinity (K d ) for binding of ␦-subunit to the ␣ 3 ␤ 3 ␥⑀ complex of E. coli F 1 -ATPase. The assay is a true equilibrium method that depends on enhancement of the fluorescence of the natural Trp at residue ␦28 in the ␦-subunit upon binding to F 1 . No chemical modification was required, although removal of some of the intrinsic Trp residues in F 1 helped to reduce the signal/noise ratio. Because purified E. coli ␦-subunit occurs as a monomer (40) the assay was not complicated by formation of dimers or aggregates of ␦ (cf. Ref. 50). Using the assay we determined the K d for binding of wild-type ␦ and of a fragment of ␦Ј, which lacks the C-terminal 43 residues, and also the affinity of binding of two mutants that impair binding, namely ␣G29D and ␦W28L. Further we demonstrate large effects of Mg 2ϩ ions and pH on the binding affinity.  We found that the K d of binding of ␦-subunit to F 1 was around 1.4 nM (Table II). A similar value was found for the chloroplast ␦-subunit binding to chloroplast F 1 (50) using an assay involving fluorescence correlation spectroscopy of chemically modified ␦. A K d value of 1.4 nM suggests a standard free energy of binding of 50.2 kJ/mol, which, as pointed out in Ref. 50 is consistent with the strain demands placed upon the stator by the torque energy generated by the rotor during ATP hydrolysis under conditions of ATP, ADP, and P i concentrations within the cell, equivalent to ϳ50 kJ/mol (50,51). We found that the ␦Ј fragment, lacking the C terminus of ␦, bound with the same affinity as intact ␦, suggesting that the C-terminal residues contribute little binding energy. Previous proteolytic cleavage of ␦ had suggested that the C-terminal region was not responsible for F 1 -binding (29). It is thought that the C-terminal region of ␦ binds to the C-terminal region of the b-subunit (21, 24 -26). A fragment of the b-subunit containing the Cterminal region, named "b sol ," was found to form a b 2 ␦ complex with purified ␦-subunit, but the binding affinity between b 2 and ␦ was surprisingly weak with K d ϭ 5-10 M (40). This would also imply that the C-terminal region of ␦ through its association with b-subunit confers little binding energy to stator resistance. However, mutations and truncations at the C-terminal region of ␦ bring about large functional deficiencies (30,52). One explanation could be that there is a cooperative effect between binding of ␦ to F 1 and to b-subunit, which tightens the overall binding of ␦. The availability of the assay described here should allow this to be examined in future work. Additional effects on stator resistance could also derive from interactions between b-subunit and ␣/␤ pairs as seen in Refs. 24 and 53. In this context, experiments on OSCP, 2 the mitochondrial homolog of E. coli ␦-subunit, are relevant. Cross-linking and proteolysis studies indicate that, like E. coli ␦, OSCP binds to the N-terminal region of ␣ and also to ␤ at the top of F 1 (54,55). Numerous functional studies indicate a similar role for the two proteins in binding F 1 to F o . However, reported K d values for binding of OSCP to mitochondrial F 1 are in the 50 -80-nM range (56,57), which is much higher than we saw here for ␦-binding in E. coli enzyme and explains why OSCP does not co-purify with F 1 in contrast to ␦. When OSCP binding to mitochondrial F 1 F o was measured, the apparent K d value was 1.7-5 nM, showing that there was an extra effect (58,59). In mitochondrial F 1 F o there are several supernumerary subunits, not seen in the E. coli enzyme, which could contribute to the higher binding affinity, but the alternative explanation, of cooperativity of binding of OSCP in F 1 F o , is also possible. Reduction of the binding affinity in the ␦W28L mutant to K d ϭ 4.6 nM (Table II) reduces the standard free energy of binding by 2.9 kJ/mol. This was not enough to have a detectable effect on function as measured by growth yield assay in whole cells or by ATP-driven proton pumping assays in vitro. However it did facilitate removal of the ␦-subunit by gel filtration at high pH, which we were able to exploit to prepare ␦-depleted F 1 . The ␣G29D mutation had a much larger effect, with the K d value being 25.5 nM (Table II), yielding a reduction in binding energy of 7.2 kJ/mol. This mutation has quite strong debilitating effects on rotation-based energy transmission between F 1 and F o . This result exemplifies how energetically finely balanced the stator stalk is, in that it is able to tolerate only very small changes in binding affinity between ␦ and F 1 .
The results with ␣G29D enzyme confirm that this residue is located at or very close to the ␦-binding site. X-ray structures (15,32) show this residue close to the surface of the N-terminal ␤-barrel domain. Whether the effect of the mutation is due to an electrostatic effect of insertion of a carboxyl or due to a poorer fit of binding surfaces after inserting the larger sidechain remains conjectural. The development of the assay system described here should now accelerate understanding of the structure of the ␦/␣ interface by facilitating mutagenesis studies, and also of ␦/␤ interfaces if they are of functional significance. As noted in the Introduction the details of ␦-binding at the top of F 1 remain intriguing. ␦ binds in just one copy, potentially to three ␣-subunits or ␣/␤ pairs. Possibly it needs only to bind to one ␣ with high affinity to achieve the proper structure. Possibly the three N termini of ␣ form a tripodal binding site, like the legs of a lunar module, with all three N termini combining to form one binding site for ␦.
The effect of the ␦W28L mutation on binding affinity, and especially the pronounced fluorescence enhancement response of residue ␦Trp-28 upon binding of ␦, indicate a location of this residue close to F 1 . The NMR structure of ␦ (27) shows that residue ␦28 lies in helix 2 (residues 24 -39) at the protein surface, but with the side-chain pointing into the protein matrix, consistent with the relatively unpolar environment reported by the Trp spectrum. One model would be that helix 2 of ␦ binds directly to F 1 , and that the substitution ␦W28L causes small conformational changes of the helix surface contours. This, however, does not agree well with the finding that residue Arg-94 of OSCP (equivalent to ␦Arg-85) is crucial for binding (57). ␦Arg-85 is located in a turn after helix 5, which consists of residues 71-83. The structure suggests also a second model, that the surface formed by residues from helix 1 (residues 5-20) and helix 5 might bind to F 1 . Side-chains from helix 1 make contact with ␦Trp-28, thus mutation of the latter might affect the binding surface through helix 1. Both binding models, but particularly the second, would decrease accessibility of ␦Trp-28 from the medium upon binding, as suggested by the 2 The abbreviation used is: OSCP, oligomycin sensitivity conferral protein.
blue-shift of fluorescence upon binding (Fig. 3). Future mutagenesis of ␦-subunit coupled with the quantitative assay should define a binding model.
Release of F 1 from E. coli membranes in soluble form is achieved in the presence of EDTA to chelate Mg 2ϩ ions, and reconstitution of F 1 F o in vitro requires the presence of Mg 2ϩ ions. The data in Table III show a large effect of Mg 2ϩ ions on the affinity of binding of ␦ to ␦-depleted F 1 and provide an explanation for the above effects. At all pH values tested, K d was higher in the presence than in the absence of Mg 2ϩ . This phenomenon was first recognized by Abrams and colleagues (60) who showed using Streptococcus faecalis F 1 that ␦-subunit was lost on gel electrophoresis in the absence of Mg 2ϩ but remained bound to F 1 in presence of 2 mM Mg 2ϩ . They concluded that Mg 2ϩ (or another divalent cation) was naturally present in the enzyme to act as an anchor between ␦ and F 1 . The data reported here confirm and extend the earlier work by showing a substantial effect of Mg 2ϩ on ␦ binding. Speculatively, one can propose that Mg 2ϩ ions bridging ␣ and ␦ are involved in binding ␦ to F 1 (60). Studies on E. coli F 1 determined that, as purified, it contained 2 Mg 2ϩ /F 1 (mol/mol) with no other metal present (61). Intriguingly, isolated ␣-subunit was found to bind 1 Mg 2ϩ (mol/mol). Furthermore, it was shown later that purified E. coli F 1 preparations commonly contain only 0.65 mol ␦/mol F 1 due to loss of ␦ during purification (62). This would imply that the true content of ␣-␦ bridging Mg 2ϩ ions might be 3 mol/mol F 1 , i.e. one per ␣. It is an interesting speculation. The data in Table III also affirm the large effect of raising pH values on weakening of ␦-binding, an effect that was recognized empirically in the past and used to deplete F 1 of ␦-subunit (43). It is clear that protonatable residues on ␣ or ␦, with pK a values in the range of 8 -9, are involved with or at least strongly influence ␦-binding.
Summarizing, we report an assay for quantitative determination of binding of ␦-subunit to F 1 -ATPase. We show that mutations in ␣or in ␦-subunits affect the K d , and that the stator is finely balanced in terms of its resistance to strain since relatively small changes in K d of ␦ binding significantly impair function. We show that the C-terminal residues of ␦ contribute no binding energy at all. Mg 2ϩ is a critical component of ␦-binding, suggesting possible ␣-␦ bridging metal site(s) in the enzyme, and high pH greatly decreased K d , implicating protonatable side-chains in the binding site. The availability of a simple but quantitative assay for ␦-binding now opens up the possibility of defining structure/function of the ATP synthase stator in detail.